wrong  0  1  2  3  4  5  6  7  8  9  10  11  12  13  Group Name:  
right  64  63  62  61  60  59  58  57  56  55  54  53  52  51  
score  100  98.4  96.9  95.3  93.8  92.2  90.6  89.1  87.5  85.9  84.4  82.8  81.3  79.7  . 
Scientist at Work  Name____________________________ 
Observation: Organisms have parts which can be measured in terms of length. Suppose you previously made some measurements on yourself. With those measurements in mind, you would now have a "human ruler." You could measure a centimeter at a time with one of your fingernails, and could measure longer lengths by "walking" with your thumb and index finger.
Which of your fingernails comes closest to 1 cm in width? 
Right Left  Thumb Index Middle Ring Pinkie 
What is the length between your thumb tip and extended index finger tip?  cm 
Width across knuckles of: left hand  cm ... right hand  cm 
Was this really an experiment?  Yes No 
If no, why not? 

If this is not an experiment, what is it? 
The width of my left hand is: 
wider than the same as narrower than  that of my right hand. 
The hypothesis: "My hands are the same size" is:  rejected not rejected 
Did the prediction thoroughly test the hypothesis?  Yes No 
If not, what else might we measure to more thoroughly test the hypothesis? (hint: the key word is "size"!)  1. 
2. 
 /13 
Observation: You now know something about your own two hands. You also notice that not everyone in the room is the same size overall.
Question: In spite of different absolute body sizes, does everyone have hands of equal width?
Hypothesis: The human population has hands of equal width.
Prediction: If the human population has hands of equal width, then a sample of the human population should have hands of equal width.
Notice that we cannot go out and measure the hands of the entire human population, so we must settle for a sample. We hope we can take a representative sample (that is a random sample). Our sample will be all the people in this laboratory.
Would this be a random sample of the population?  Yes No 
If it is not a random sample, why isn't it? 
We also hope that our sample is sufficiently large. In spite of any shortcomings in our sample, we will continue our analysis since we lack a better sample.
Experiment: Your instructor will help you post your hand width data along with your classmates' on the blackboard.
By collecting lots of data, do we now have an experiment?  Yes No 
If no, why not? 
If this is not an experiment, what is it? 
Analysis: Clearly we have various widths in each sample and must now include an assessment of this variation in preparing for our decision. Calculate the mean (average) width and the standard deviation of the samples. The latter gives us some measure of the variation (or spread) around the mean. Most calculators will determine the mean and standard deviation using the formulae shown below for you, but we will let a computer do this work for us!
Mean = x = 
n ∑ i=1  x_{i} 
Standard Deviation = s = 
√ 
n (∑ i=1  x_{i}^{2} )  x ^{2}n  

n  n1 
Left hands in sample:  Right hands in sample:  
Mean Width (cm):  
Standard Deviation (cm): 
 /9 
Ttable  

Degrees of Freedom  Critical Levels  
0.10  0.05  0.01  
1  6.314  12.706  63.657 
2  2.920  4.303  9.925 
3  2.353  3.182  5.841 
4  2.132  2.776  4.604 
5  2.015  2.571  4.032 
6  1.943  2.447  3.707 
7  1.895  2.365  3.499 
8  1.860  2.306  3.355 
9  1.833  2.262  3.250 
10  1.812  2.228  3.169 
11  1.796  2.201  3.106 
12  1.782  2.179  3.055 
13  1.771  2.160  3.012 
14  1.761  2.145  2.977 
15  1.753  2.131  2.947 
16  1.746  2.120  2.921 
17  1.740  2.110  2.898 
18  1.734  2.101  2.878 
19  1.729  2.093  2.861 
20  1.725  2.086  2.845 
21  1.721  2.080  2.831 
22  1.717  2.074  2.819 
23  1.714  2.069  2.807 
24  1.711  2.064  2.797 
25  1.708  2.060  2.787 
26  1.706  2.056  2.779 
27  1.703  2.052  2.771 
28  1.701  2.048  2.763 
29  1.699  2.045  2.756 
30  1.697  2.042  2.750 
40  1.684  2.021  2.704 
60  1.671  2.000  2.660 
120  1.658  1.980  2.617 
∞  1.645  1.960  2.576 
We will let a computer determine the tstatistic for our samples. The formula it is using assumes n_{1}=n_{2}.
(x_{1} x_{2}) √n  =  

√s_{1}^{2} + s_{2}^{2} 
Ignore any negative sign carried by the tstatistic.
This tstatistic is compared with a value in a ttable.
The table value is found by using a row defined by the degrees of freedom:
N_{1} + N_{2}  2 = 
and a column defined by the acceptable level of error. As scientists, what level of error is acceptable? Most scientists admit that 5% of the time chance alone will explain errors. Our table includes a 5% column.
Circle the pertinent table value in the table → → →
Decision Rules:
If the tstatistic is greater than the table value, the two samples are significantly different.
If the tstatistic is less than or equal to the table value, then the samples are statistically the same.
Based upon Student's Ttest, the hypothesis:  
"The human population has hands of equal width" is:  rejected not rejected 
There are two reasons for this decision:  
The statistical test tells us:  
The sample providing the data was: 
 /6 
Observations: A single bag of beans was purchased from the store. Some of the beans were soaked in water overnight, the rest from the same bag remain dry. Clearly the soaking has had some effect upon length.
Question: Does soaking beans cause them to expand?
Hypothesis: Soaking causes beans to expand.
Prediction: If soaking causes beans to expand, then beans will be significantly larger when they are soaked than beans which have been kept dry.
Experiment: A sample of beans was divided into two subsamples. One subsample was placed in water, the other subsample was kept in dry conditions. Use a balance to its greatest precision to determine the weight of each of 10 beans from each subsample.
Soaked Beans  Dry Beans 

Was this really an experiment?  Yes No 
If no, why not? 

If this is not an experiment, what is it? 
Soaked Beans  Dry Beans  

Mean Weight (g)  g  g 
Standard Deviation 
Analysis: Carry out a ttest to see whether there is any significant difference between the two subsamples.
Tstatistic:  Degrees of Freedom:  Table Value: 
Based on the ttest, are the two means significantly different?  Yes No 
Decision:
Based upon Student's Ttest, the hypothesis:  
"Soaking causes beans to expand" is:  rejected not rejected 
Our hypothesis used the term "expand" and our prediction used the term "larger." In our experiment we tested the weight of the soaked beans.
What weight adjective would describe the soaked beans? 
 /15 
Soaked Beans  Dry Beans  

Final Liquid Level  mL  mL 
Starting Liquid Level   14 mL   14 mL 
Total Volume of Beans Added  mL  mL 
Number of Beans Added  beans  beans 
Volume per Bean  mL/bean  mL/bean 
Was this really an experiment?  Yes No 
The group of dry beans receiving no treatment is the  group.  
The group of soaked beans is called the  group. 
Can we perform a Ttest on these data?  Yes No 
If No, why not? 
If we wanted to redo our volume measurements, how could we do them so that we could use a statistical test for our analysis? 
Calculate the ratio of the volume per soaked bean to the volume per dry bean. 
The soaked beans occupy  %  of the volume of the dry beans. 
Is there at least a 5% difference between the beans?  Yes No 
Based upon a displacement test, the hypothesis:  
"Soaking does not cause beans to expand" is:  rejected not rejected 
Why did we choose to rewrite our hypothesis this time to its alternate "no effect" form? 
By having our hypotheses rejected, are we poor scientists?  Yes No 
Why did we not have the option to "prove" any of our hypotheses? 
 /21 
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